Polarons and charge transfer in FeCr$_2$O$_4$ chromite treated by the $\mathrm{DFT} + U$ method

The electronic structure of chromite (FeCr$_2$O$_4$ spinel) is described and the orbital ordering, band gap, and charge transfer are analyzed consistently in the framework of density functional theory taking into account strong electron correlations ($\mathrm{DFT} + U$ method). It is shown that the top of the chromite valence band in this model is formed by the ordered $t_{2g}$ orbitals of iron atoms located at tetrahedral sites, and the formation of hole polarons occurs involving just these orbitals. The nonadiabatic activation barrier determining the hole polaron transport is considered. The results of calculations of the band gap and activation energy are compared to the available experimental data.